(Renatus Cartesius), philosopher and scientist, born at La Haye France, 31 March, 1596; died at Stockholm, Sweden, 11 February 1650. He studied at the Jesuit college of La Flèche, one of the most famous schools of the time. In 1613 he went to Paris, where he formed a lasting friendship with Father Mersenne, O. F. M., and made the acquaintance of the mathematician Mydorge. He afterwards enlisted in the armies of Maurice of Nassau, and of the Duke of Bavaria. On 10 November, 1619, he felt a strong impulse to set aside the prejudices of his childhood and of his environment, and to devote his life to the restoration of human knowledge, which was then in a state of decadence; and for him this mission took on quite a mystical character. He had a dream which he interpreted as a revelation, and he became convinced that "it was the Spirit of Truth that willed to open for him all the treasures of knowledge". After much journeying in Brittany, Poitou, Switzerland, and Italy, he returned to Paris in 1625. There he remained for two years during which it was his fortune to meet Cardinal Bérulle who encouraged him in his scientific vocation. But as Paris offered neither the peace nor the independence his work demanded, he set out in 1629 for Holland, and there in the midst of a commercial people he enjoyed the advantage of living as quietly as in a desert. From this retreat he gave to the world his "Discours de la méthode" (1637), "Méditations" (1641), "Principes" (1644), and "Passions"(l649). "Le Monde" had been completed in 1633, but the condemnation of Galileo frightened Descartes who preferred to avoid all collision with ecclesiastical authority. He deferred the publication of this clever work without, however, losing hope of eventually bringing it out. In 1649, yielding to the entreaties of Queen Christina, he went to Sweden, and died at Stockholm of inflammation of the lungs.

Descartes' work is important rather because of its quality than of its quantity. Let us see first of all wherein his method is new. He observed, as Bacon had already done before him, that there is no question on which men agree. "There is nothing", he says "so evident or so certain that it may not be controverted. Whence then this widespread and deep-rooted anarchy? From the fact that our inquiries are haphazard" (Règles pour la direction de l'esprit, 4e Règle). The first problem, then, is to discover a scientific method. How is success in this difficult task to be assured? To begin with, we must cease to rely on authority; and for two principal reasons. "In whom can we trust" when "there is hardly a statement made by one man, of which the opposite is not loudly supported by some other?" And even "if all were agreed, the knowledge of their teaching would not suffice us." "Had we by rote all the arguments of Plato and Aristotle, we should not be any the more philosophers unless we were able to bring to bear on any given question a solid judgment of our own. We should have indeed learned history but not mastered a science" (3e Règle) Philosophy presupposes the understanding of problems—and consequently its method cannot be external, it must be essentially immanent. The true method is to seek for reasonable evidence and the norm of such evidence is to be found in the science of mathematics (Discours de la méthode, 2e partie). "It is not that arithmetic and geometry are the only sciences to be learned, but that he who would progress on the road to truth must not delay over any object about which he cannot have a certainty equal to that given by arithmetical and geometrical demonstrations" (2e Règle).

Is everything, then, capable of being known in this way, and consequently can human knowledge become the complete counterpart of reality? Descartes says so over and over again; it is his controlling idea; and he endeavours to prove it both from the nature of our thought and from the universal connexion of things. The mind is equally intelligent however diverse the objects it considers; and those objects because of their perfect enchainment are always equally intelligible. There is, therefore, no question "so far removed from us as to be beyond our reach or so deeply hidden that we cannot discover it", provided only that we persevere and follow the right method (Disc. de la méth. 2e partie; 4e Règle). Such is the rationalism of Descartes, surpassing even that of Plato, in which under the name of "the Infinite" three-fourths of reality remains for ever unknowable. How then is this mathematical evidence to be obtained. Two methods, dangerous at once and sterile, must be avoided. We cannot build on the experience of our senses; "for they are often deceptive", and consequently need a control which they have not in themselves. Bacon was misled on this point (2e Règle). Neither can we adopt the syllogistic method; for this is not, as was formerly thought, a means of discovery. It is simply a process in which, two terms being given, we find by means of a third that the former two are linked together, i. e. that they have some common characteristic. Now if they have this common characteristic it is useless to search for it with any light other than their own. Let them pass under direct scrutiny; let their natures be studied, and in time the common trait will reveal itself. This is the mind's straight road to discovery, passing on from one idea to another without the aid of a third. The syllogism is of no use until the discovery has been made; it simply serves the purpose of exposition (14e Règle). There are but two ways leading to mathematical evidence: intuition and deduction (3e Règle). Intuition "is the conception formed by an attentive mind so clear and distinct that it admits of no doubt: or what amounts to the same thing, it is the clear conception of a sound and attentive mind, the product of unaided reason" (3e Règle). Intuition is not, therefore, perception by the senses—it is an act of the understanding brought to bear on an idea. The senses do not supply the object but merely the occasion. A movement, for instance, awakens in us the idea of motion, and it is that idea we must regard as the object of intuition. In very simple matters intuition acts quickly; thus "everyone can know intuitively that he exists; that a triangle is terminated by three angles, neither more nor less, and that a globe has but one surface" (3e Règle; 12e Règle; Rép. aux deux objections). In the case of objects more or less complex, intuition proceeds by way of analysis. Since it deals with ideas, and ideas are but one aspect of thought, everything must be reduced to clear and distinct elements, to ultimate or "indecomposable" parts. These ultimate parts must be inspected one after another, until the object is exhausted, "by passing from those that are easily known to those that are less easily known" (6e Règle). In the long run everything will be spread out in full light.

Deduction is the process in which by a continuous movement of thought we draw from a thing that we certainly know the conclusions that of necessity flow from it. This procedure may be carried on in two ways. "If, for instance, after various calculations I discover the relation between the quantities A and B, between B and C, between C and D, and lastly between D and E, I do not yet know the relation between A and E"; but I can infer it by retracting the several steps of the series. This is the first form of deduction (7e Règle). There is a second form in which, the connecting links of the series being too numerous to enter the mental field of vision all at once, we are content to draw conclusions from the general impression we have of the series (7e Règle). Deduction is an intellectual process, but it differs from intuition by bringing in memory as a factor. And this is noteworthy in view of the important role that memory plays in the Cartesian explanation of certitude, and the desperate effort he makes to defend this procedure. From the conspicuous place that reason holds in the Cartesian method, one might infer that there was no room for experience. Nothing could be less true. For Descartes, as for Bacon, the one purpose of science is utility. He also expects from it a continual betterment of the conditions of human life, and his hopes in that direction go very far, as, for instance, when he says of medicine that in the end it would procure us the boon of immortality (Disc. de la méth. 6e partie). And as he who wills the end wills the means also, Descartes accepts in its entirety the experimental part of the Baconian method (letter to Mersenne, 1631), and acts accordingly. He put himself in touch with all the experimental work of his day (letter, April, 1632), urged others to take up research (letter to Mersenne, 1632), and carried on experiments of his own that covered a wide range of subjects: the weight of air (letter, 2 June, 1631), the laws of sound and light (letter, 1633); the essential differences between oils, spirits, eaux-de-vie, common waters, aquafortis, and salts. He dissected the heads of various animals to show the workings of memory and imagination (cf. letters to Mersenne, 1633 April, 1637; 13 November, 1639; 4 January, 1643, ed. Cousin, Paris, 1826). There was hardly a fact that escaped this apologist of Reason nor anything into whose hidden nature he did not inquire; even the "Chasse de Pan" he followed with his accustomed ardour.

But if the mind, moving as it does in the realm of intelligible objects, have a power of intuition sufficient to master them all, why these researches? Are they not a hindrance rather than a help? Let deduction but go on to the end, and it must assuredly attain that exhaustive knowledge which is the goal of investigation, but such is not the case. Experiment helps reasoning in more ways than one. It supplies the fact that calls forth in our intelligence the idea of the problem to be solved. That idea once aroused, the intelligence takes hold of it, and may produce many others, according to the nature of which experience and reason play reciprocal, yet different, roles. The idea of a problem may be so simple as to allow a mathematical deduction of the properties of the object in question and nothing more. In this case experiment is called in only by way of illustration, as happens, for instance, in the study of the laws of motion. (Cf. Principes, 2e partie.) But again the idea of a problem may be so complex as to suggest various hypotheses, since principles as a rule are so fruitful that we can draw from them more than we see in the world around us. We must then choose from among the hypotheses presented by the intellect that which corresponds most nearly to the facts: and experiment is our only resource. It acts as a sort of guide to rational deduction. It sets up, so to say, a number of sign-posts which point out, at the cross-roads of logic the right direction to the world of facts. Finally, we may be confronted with two or more hypotheses equally applicable to the known facts, observations must then be multiplied until we discover some peculiarity which determines our choice: and thus experiment becomes a real means of verification (Principes, 4e partie.) In every case experiment is, as it were, the matter, while calculation becomes the form. In the physical world there is nothing but motion and extension, nothing but quantity. Everything can be reduced to numerical proportions, and this reduction is the final object of science. To understand means to know in terms of mathematics. When this final stage is reached, intelligence and experience unite in closest bonds: the intellect setting its seal on experience and endowing it with intelligibility.

Such is the method of Descartes. There remains to be seen what use he makes of it. Recourse must be had to provisional doubt as the only means of distinguishing the true from the false in the labyrinth of contradictory opinions which are held in the schools and in the world at large. We must needs imitate those builders who, in order to erect a lofty structure, begin by digging deep, so that the foundations may be laid on the rock and solid ground (Remarques sur les 7es objections, ed. Charpentier, Paris; cf. Disc. de la m´thode, 3e partie.) And this provisional doubt goes very deep indeed. We may reject the evidence of the senses for they are deceptive, "and it is but the part of prudence never to trust absolutely what has once deceived us" (1re Méditation). We may even question whether there be "any earth or sky or other extended body"; for, supposing that nothing of the sort exist, I can still have the impression of their existence as I had before; this is plain from the phenomena of madness and dreams. What is more, the very simplest and clearest truths are not free from suspicion." How do I know that God has not so arranged it that I am deceived each time I add two and three together, or number the sides of a square, or form some judgment still more simple, if indeed anything more simple can be imagined" (3e Méditation). What then remains intact? One thing only, the fact of my thought itself. But if I think it is because I exist, for from the one to the other of these terms we pass by simple inspection— Cogito, ergo sum: Behold the long-sought rock on which the edifice of knowledge must be built (Disc. de la méth., 4e partie, 2e Méd.). But how is this to be done? how are we to make our way out of the abyss into which we have descended? By analysing the basic fact, i. e. the content of our thought. I observe that, since my thought gropes amid doubt, I must be imperfect: and this idea calls forth this other, viz. of a being that is not imperfect, and therefore is perfect and infinite (Disc. de la méth., 4e partie.) Let us consider this other idea. It must necessarily include existence otherwise something would be wanting to it; it would not be perfect or infinite. Therefore, God exists, and "I know no less clearly and distinctly that an actual and eternal existence belongs to His nature than I know that whatever I can demonstrate of any figure or number belongs truly to the nature of that figure or number " (Disc. de la méth., 4e partie; 5e Médit.; Rép. aux premières obj.).

God, therefore, is known to us at the outset, the moment we take the trouble to look into the nature of our own minds; and this is enough to eliminate the hypothesis of an evil genius that would take pleasure in deceiving us; it is enough also to secure the validity of all our deductions, whatever be their length, for "I recognize that it is impossible that He should ever deceive me, since in all fraud and deceit there is a certain imperfection" (4e Méd.). Otherwise how would this idea of God be anything more than an idle fancy? It has immensity; it has infinity, and therefore it must of itself be capable of existing. Spinoza, and after him Hegel, will teach that the possible infolds, as it were, an essential tendency to existence, and that this tendency is greater in proportion as the possible is perfect. It is on this principle that they will build their vast synthetic systems. Descartes anticipates them and when closely pressed he replies just as do these later philosophers. (Rép. aux premières objections.) It is a fact worth noting with reference to the genesis of modern systems.

The presence in us of this idea of God must also be explained; and here we find a new ray of light. The objective reality of our ideas must have some cause, and this is readily found when there is question of secondary qualities; these may be illusory or they may result from the imperfection of our nature. The question also can be solved without too much difficulty when it concerns primary qualities. May not these arise perchance from some depth of my own mental being that is beyond the control of my will? But such explanations are of no avail when we try to account for the idea of a being infinite and perfect. I myself am limited, finite; and from the finite, turn it about as we may, we can never derive the infinite the lesser never gives us the greater (3e Méd. cf. Princ., 7e partie). Considered from any and every point of view, the idea of God enlightens us as to His existence. Whatever the manner of our questioning it gives us always from the depth of its fulness the one reply, Ego sum qui sum. Since then the veracity of God Himself guarantees our faculties in their natural exercise, we may go forward in our inquiry; and the first question that meets us concerns the subject in which the process of thought takes place, i.e. the soul. Understanding, conceiving, doubting, affirming, denying, willing, refusing, imagining, feeling, desiring—these are the activities of what I call my soul. Now all these activities have one common quality: they cannot take place without thought or perception, without consciousness or knowledge. Thought then is the essential attribute of the soul. The soul is "a thing that thinks" (2e Méd., Princ., 1re partie) and it is nothing else. There is no substratum underlying and supporting its various states; its whole being issues in each of its activities; thought and soul are equivalent (12e Règle).

Is thought, then, always in some mode of activity? Descartes leans to the belief that it is. "I exist", he says, "but for how long? Just as long as I am thinking; for perhaps if I should wholly cease to think, I should at the same time altogether cease to be" (2e Méd.). It is only with reluctance and under the pressure of objections that he concedes to the soul a simple potentia or power of thinking (5es Obj.); and, as may be easily seen, the concession is quite illogical. Thought, though in itself a unitary process, takes on different forms; it begins with confused ideas or perceptions which require the co-operation of the body; such are the feelings of pleasure and pain, sensations imagination, and local memory. Then the soul has clear and distinct ideas, which it begets and develops within itself as immanent activities. Under this head come the ideas of substance, duration, number, order extension, figure, motion, thought, intelligence, and will (6e Méd.; Princ., I).

These clear and distinct notions constitute of themselves the object of the understanding, and one may say that they are all involved in the idea of perfect being. Whether I understand, or pass judgment or reason, it is always that idea which I perceive and my understanding could have no other object, seeing that its sphere of action is always the infinite, the eternal and the necessary. To advance in knowledge is to progress in the knowledge of God Himself. (Rep. aux 2es obj.) But thought has another dominant form, viz. freedom. For Descartes this function of the mind is a fact "of which reason can never convince us", but one which "we experience in ourselves", and this fact is so evident" that it may be considered one of the most generally known ideas" (Rep. aux 3es obj.; Rep. aux 5es obj.- Princ., 1re partie). Not only is this freedom a primordial and undeniable datum of consciousness: it is, in a way, infinite like God, "since there is no object to which it cannot turn". (4e Méd.; Princ., 1re partie.) It does not creep round in a sort of semi-ignorance, as St. Thomas Aquinas holds, but it grows as the influencing motives become clearer; indifference is but its lowest stage (letter to Mersenne, 20 May, 1630). The part it plays in our lives is considerable: it enters into each of our judgments, and it is the formal cause of all our errors. It makes itself felt in every part of our organism, and through this it influences the external world. Nevertheless, the sum total of motion in the world is always constant; for while our wills may change the direction of movement they do not affect its quantity. (Letter to Regius.) Confronting the soul is the external world: but the soul does not see it as it really is. Heat, odour taste, light, sound, resistance, weight are qualities which we attribute to bodies but which are really in ourselves, since we only conceive them in relation to ourselves. In reality there is nothing in the physical world but motion and extension. Motion imitates as far as possible the immutability of God who is its first cause; hence its principal laws, viz. that the sum of motion in the world is always constant; that a body will continue in its actual state unless disturbed by some other body outside itself; that "once a body is in motion we have no reason for thinking its present velocity will ever cease provided it impinges on no other body which would slacken or destroy its motion". All movement is primarily rectilinear (on this point Aristotle was mistaken). When two bodies moving in different directions collide, a change takes place in their directions, but "such change is always the least possible". When two moving bodies impinge on each other, one cannot transmit any motion to the other without losing what it transmits (Princ., 2e partie). Extension is not infinite in duration but it is infinite in space. "It seems to me that one cannot prove or even conceive that there are limits to the matter of which the world is composed, for I find it is composed of nothing but extension in length, breadth, and depth. So that whatever possesses these three dimensions is a portion of such matter": and however far back in imagination we push the limits of space we still find these three dimensions; they are bounded by no limits (letter to Chanut; letter to Marus). Extension is therefore one block, continuous from end to end; and this proves at the same time that there is no such thing as a vacuum, either in bodies or between them. Moreover extension is divisible ad infinitum since the divided particles, however small, are still extended. It is everywhere homogeneous, since it is made up of spatial dimensions only, and these of themselves give rise to no qualitative differences. And this brilliant idea suggested to Descartes many hypotheses that were to prove fruitful. In his view the matter of the earth and of the stars was the same; and spectrum analysis subsequently proved that he was correct. He held that the primordial state of the sun and planets was nebulous, that under the influence of a cooling process the heavenly bodies formed their crusts, and to changes in these crusts is due the variation in brilliance of the stars and the emergence of the continents on our earth. (Cf. Traité du Monde; Princ., 3e and 4e p.) It does not follow that the world is self-sufficient; but the finality, of which so much is said, leads to nothing. God gave matter a first impulse and the rest followed in the course of nature's laws. "Even if the chaos of the poets be granted, one could always show that, thanks to the laws of nature, this confusion would eventually work itself out to our present order"; the laws of nature being such that "matter is constrained to pass through all the forms of which it is capable".

The older Descartes grew, the more he busied himself with morals, and his aim was to end up with a treatise on ethics. As a matter of fact, we have his treatise on the passions, and a few brief disquisitions scattered among his letters to Chanut and to the Princess Elizabeth. The passions are perceptions generated and nurtured in the soul "through the medium of the nerves" (Passions, 1re partie, art. 3-22). The nerves are bundles of fine threads: these threads contain the animal spirits which are the subtlest parts of the blood: and they all meet at the pineal gland which is the seat of the soul. By means of this mechanism the thinking subject receives impressions from the world without, perceives them, and transforms them into passions (Pass., 1re p, art. 31). And though our organism thus contains the cause of our passions, it is not their subject either entirely or partially; on this point also Aristotle was mistaken. There are perceptions arising from the body and localizing themselves in one or other portion of it—such as hunger, thirst, pain—but the passions are different. They originate in the body, but belong to the soul alone; they are purely psychological facts (Passions, 1re p., art.25). There are as many passions as there are ways in which objects capable of affecting our senses may be hurtful or profitable to us. The primary passions to which all others may be reduced are the six following:

admiration or surprise, produced by an object as to which we are as yet ignorant whether it is useful or hurtful;

love and hate, caused by the impression produced on our organs of sense by objects which are already known to us as beneficial or harmful;

desire, which is but the love or the hate we bear an object considered as future;

joy and sadness, which result from the presence of an object that is loved or hated (Passions, 2e partie, art. 52).

Perhaps on the whole St. Thomas and Bossuet will be found to have surpassed Descartes, by reducing all the passions to love. In the Cartesian teaching the passions are good in themselves, but they must be kept in subjection to the law of moral order. What this law is he does not clearly indicate; he gives only some scattered precepts in which one may discern a noble effort to build up a Stoico-Christian system of ethics. The foregoing account may perhaps give the impression that Descartes was a great savant rather than a great philosopher; but the significance of his scientific work should be properly understood. What remains of value is not so much his theories, but the impetus given by his genius, his method, his discoveries. His quantitative conception of the world is being gradually abandoned, and today men's minds are turning to a philosophy of nature wherein quality plays a controlling part.